Problem: Nadia is 4 times as old as Ashley. Six years ago, Nadia was 6 times as old as Ashley. How old is Nadia now?
Solution: We can use the given information to write down two equations that describe the ages of Nadia and Ashley. Let Nadia's current age be $n$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $n = 4a$ Six years ago, Nadia was $n - 6$ years old, and Ashley was $a - 6$ years old. The information in the second sentence can be expressed in the following equation: $n - 6 = 6(a - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = n / 4$ . Substituting this into our second equation, we get: $n - 6 = 6($ $(n / 4)$ $- 6)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $n - 6 = \dfrac{3}{2} n - 36$ Solving for $n$ , we get: $\dfrac{1}{2} n = 30$ $n = 2 \cdot 30 = 60$.